David Little
Mathematics Department
Penn State University
Eberly College of Science
University Park, PA 16802
Office: 403 McAllister
Phone: (814) 865-3329
Fax: (814) 865-3735
e-mail:dlittle@psu.edu

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Euclidean Geometry


Download this applet for off-line viewing.

None
Drag any movable point (represented by a dot) to a different position or click on any point (dot or cross), line and/or circle to change it's color.

Point
Click anywhere on the applet to create a new movable point. You may also drag any pre-existing movable point to a new position. If the mouse is over a point, the point will be highlighted.

Line
Click on any two distinct points, A and B. Draws the line through A and B. If you click on the screen, a new point will be created at that point, if none already exists there.

Line Segment
Click on any two distinct points, A and B. Draws the line segment with endpoints A and B. For the purposes of the following descriptions, a line segment is considered to be a line while a line is not a line segment.

Circle
Click on any two distinct points, A and B. Draws the circle centered at A that goes through B. If you click on the screen, a new point will be created at that point, if none already exists there.

Intersection
Click on any two lines and/or circles. If the two objects you selected intersect, the points of intersection will be drawn. In the case of the intersection of a line and a circle or the intersection of two circles, this may result in two points of intersection.

Angle Bisector
Click on any three distinct points, A, B and C. Draws the line which bisects the angle ABC. See Bisecting An Angle.

Centroid
Click on any three distinct points, A, B and C. Draws the centroid of the triangle with vertices A, B and C. See Centroid.

Circumcenter
Click on any three distinct points, A, B and C. Draws the circumcenter of the triangle with vertices A, B and C. See Circumcenter.

Circumscribed Circle
Click on any three distinct points, A, B and C. Draws the circle through through A, B and C.

Equilateral Triangle
Click on any two distinct points, A and B. Draws an equilateral triangle with side AB. The triangle is drawn so that vertex A immediately precedes B when reading the vertices in counterclockwise order. See Constructing An Equilateral Triangle.

Euler's Line
Click on any three distinct points, A, B and C. Draws Euler's line of the triangle with vertices A, B and C. See Euler's Line.

Incenter
Click on any three distinct points, A, B and C. Draws the incenter of the triangle with vertices A, B and C. See Incenter.

Inscribed Circle
Click on any three distinct points, A, B and C. Draws the circle of maximum area that fits inside the triangle with vertices A, B and C.

Inversion
Click on a point A and a circle C. Draws the inversion of point A across circle C. In other words, it draws the unique point B such that |OA||OB| = R2 where O is the center of the circle and R is the radius of the circle. See Inversion of a point across a circle.

Midpoint
Click on any two distinct points, A and B. Draws the midpoint of A and B. See Constructing The Midpoint.

Orthocenter
Click on any three distinct points, A, B and C. Draws the orthocenter of the triangle with vertices A, B and C. See Orthocenter.

Parallel Line
Click on a point A and a line L. Draws the line through A and parallel to L. See Constructing A Parallel Line.

Perpendicular Bisector
Click on a line segment L, with endpoints A and B. Draws the line through the midpoint of A and B perpendicular to L. See Constructing The Perpendicular Bisector.

Perpendicular Line
Click on a point A and a line L. Draws the line through A and perpendicular to L. See Constructing A Perpendicular Line.

Point on Line
Click on a line L. Draws a movable point on L.

Point on Circle
Click on a circle C. Draws a movable point on C.

Projection
Click on a point A and a line L. Draws the point on L that is closest to A. In other words, it draws the intersection of L and the line through A perpendicular to L. See Projecting A Point Onto a Line.

Reflection
Click on a point A and a line L. Draws the reflection of point A across line L. In other words, it draws the point that is the mirror image of A on the opposite side of L. See Reflection of a point across a line.

Square
Click on any two distinct points, A and B. Draws a square with side AB. The square is drawn so that vertex A immediately precedes B when reading the vertices in counterclockwise order.